Geometric methods in statistical learning theory and applications

统计学习中的几何方法理论与应用

• 批准号: 391056645
• 负责人: Professor Dr. Lorenz Schwachhöfer
• 金额: --
• 依托单位: Institute of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/391056645?language=en
• 关键词: Geometric; methods; statistical; learning; theory

This project aims at developing differential geometric methods in statistical learning theory, in particular in the geometry of efficient estimators. When investigating large amounts of data, it is essential to find a density function representing the structure of the data. This is done by giving a so called estimator, based on some feature function of the data. The efficiency of this estimator is then defined in terms of the deviation of the estimated from the actual density.In recent years, differential geometric methods were developed for constructing efficient estimators, and it is the aim of the present project to refine these methods. In particular, we wish to investigate exponential models and the geometry of the natural gradient flow, and apply them to machine learning.

该项目旨在发展统计学习理论中的微分几何方法，特别是有效估计的几何方法。在研究大量数据时，必须找到一个表示数据结构的密度函数。这是通过基于数据的一些特征函数给出所谓的估计量来完成的。这个估计的效率，然后定义在估计的偏离实际density.In近年来，微分几何方法被开发用于构建有效的估计，它是本项目的目的，以完善这些方法。特别是，我们希望研究指数模型和自然梯度流的几何形状，并将其应用于机器学习。

项目成果

Almost formality of manifolds of low dimension

低维流形的近似形式

• DOI: 10.2422/2036-2145.201905_002
• 发表时间: 2021
• 期刊: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
• 作者: Domenico Fiorenza;Kotaro Kawai;Hông Vân Lê;Lorenz J. Schwachhöfer
• 通讯作者: Lorenz J. Schwachhöfer